Challenge Yahya Abdul-Mateen II to a staring contest and he’ll almost certainly win. Chess, on the other hand? The verdict is still out.

He was partaking in both on a recent Sunday morning in Union Square Park in Manhattan, where he was playing chess against Douglas Miller, a chess teacher recommended by a friend.

Mr. Abdul-Mateen II leaned forward and fixed his opponent with a penetrating gaze, but it made little difference.In a spirited but silent exchange, he quickly lost a rook after moving a pawn forward without anticipating the opening.

He rubbed his mustache and sighed. “I should’ve seen that,” he said, whispering to himself.

His chess skills may need work, but his acting career is doing just fine, thank you. In a short amount of time, Mr. Abdul-Mateen II, 32, has made his mark as a charismatic actor, most notably in “The Get Down,” a 2016 Netflix series directed by Baz Luhrmann in which he played a disco-dancing gangster named Cadillac. And this month he will star in “Aquaman,” opposite Jason Momoa, as the superhero’s archnemesis, Black Manta.

Despite his onscreen bravado, he is attracted to quieterpastimes like chess or golf. They provide him with some much desired tranquillity.

“I can quiet myself and allow myself to shut up and think,” he said, staring intensely at the green-and-white chess board. “I really enjoy that, I enjoy silence. I find that I need it, especially in a very loud business, one that always asks me to speak, to perform.”

“But I love the spotlight, too,” he added. “I can’t go to a theater and not want to be on the stage when the lights come up. Those two things are simultaneous.”

Those opposing forces were on display on an unseasonably warm October morning, which brought teeming crowds to the park. Wearing a black beanie, a tangle of gold necklaces and a Mickey Mouse sweatshirt, Mr. Abdul-Mateen II had an air of inscrutability.

There were, however, some captivating ticks on display — covering his mouth, biting his cheeks, clearing his throat and little shrugs or laughs he shared with himself — that played like a three-act drama about how to conceal performance anxiety.

“Let’s play again,” he said, after Mr. Miller got to checkmate about 15 minutes into a game. “Maybe I have moves or patterns that you can see and help me with.”

“You need theory,” Mr. Miller said, setting up the board for another round as a group of Hare Krishnas sang and danced nearby. “Most theory is endgame, and that’s the deepest part of chess. You can easily get a piece to any position on the board, but you have to know how to use it and exploit it.” He suggested reading the book “My System” by Aron Nimzowitsch.

It would be tempting to draw parallels between the actor’s career and his chess play, but there was more luck than strategy involved with acting. “I never wanted to be, never knew that I could be, an actor,” he said. “Actors were the people on TV, inside the box.”

Mr. Abdul-Mateen II was raised in New Orleans and Oakland, Calif., the youngest of six children. Growing up, he said, his family was known as the “black Brady Bunch.” “We had the house, the dog, the station wagon,” he said. “We had a chain-link fence, though, not a white picket fence.”

When a childhood friend, Marshawn Lynch, was drafted to the National Football League, it opened his mind to more possibilities. “That was one of the first times that I saw someone that I knew inside the box, you know what I mean?” he said. “And that demystified the whole idea that the people in the box were different than me.”

Still, he pursued a more traditional path at first, attending the University of California, Berkeley, where he received a bachelor’s degree in architecture, and working as a city planner in San Francisco.

When he was laid off in 2010, he saw an opportunity to pursue his dream of acting and moved to Los Angeles. A castmate in a small community production of “Twelfth Night” was preparing to audition for graduate school, which inspired him to do the same. He aimed high and got accepted at the Yale School of Drama. His greatest lesson? “It took me three years to learn how to talk and listen,” he said.

Thanks to his brooding intensity and showman’s swagger, he quickly made inroads into Hollywood. But playing the villain in a highly anticipated holiday blockbuster is his biggest role yet. A comic book neophyte when he landed the part, he had his work cut out for him.

“I immediately went on Twitter to see what the fans loved about Black Manta,” he said. “I wanted to be able to add those things to the character. I read the comics, too, so I could develop my own perspective on who he was.”

His best insight came from Hugh Jackman, who plays Wolverine in the X-Men franchise. The two met on the set of “The Greatest Showman.” “Hugh told me, ‘You know, the villains are the best parts. You get the best lines, you work the least amount of days, and you win all the fights except for the last one,’” he said.

Next up is a role in Jordan Peele’s follow-up to “Get Out,” and a return to the world of comic books in HBO’s adaptation of “The Watchmen,” which is being produced by Damon Lindelof (“The Leftovers”).

Mr. Abdul-Mateen II declined to give away anything about those two projects, set to debut next year. “Sorry, man. I wish I could,” he said.

The chessboard was set up for a rematch. At first, he seemed to hold his own, briskly advancing his pieces forward. But soon, his knight fell, followed by the rook, the bishop and the queen. It took Mr. Miller 10 minutes this time to reach checkmate.